We study a single two-dimensional Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated to each point on the Fermi surface) coupled by a random vector potential. This low-energy theory exhibits an exactly solvable random fixed line, along which we directly compute various disorder-averaged observables without the need for the usual replica, supersymmetry, or Keldysh techniques. We find the longitudinal dc conductivity in the collisionless $\hslash \omega /k_{B}T\to \infty$ limit to be nonuniversal and to vary continuously along the fixed line.

• Received 8 November 2022
• Revised 29 March 2023
• Accepted 24 April 2023

DOI:https://doi.org/10.1103/PhysRevB.107.205145